OP THE EXPEDITION. IX 



microscopes, and with which, as expressed in your letter of 2d September, ' Declinations; 

 Bestimmungen gemacht werden, welche in Genanigkeit denen von Washington gleich komen.' 



"We have not such a spare instrument belonging to the navy. One was shown to me a few 

 years ago at Cambridge, Massachusetts, (I think,) and in 1843 Mr. William Simms told me in 

 London he had recently (then) constructed one about that size for the university at Tuscaloosa, 

 in Alabama. One or the other of these may probably be obtained for the Expedition. If they 

 cannot, or are tmsuited to the purpose, either Mr. Simms or one of your German artists could 

 construct one by next July, and I feel confident the Minister of Marine will authorize it should 

 he determine to patronise the enterprise. 



"I think additional value would be given to certain of the differential micrometer observations, 

 if they could be made at the two observatories with the same stars at the same, pre-appointed, 

 instants ; it being understood that both before and after these instants the greatest number of 

 measurements be made which the condition of the atmosphere will permit. Of course, the 

 circumstances of the refraction at the two stations will be different, but interpolations for 

 changes of declination will be avoided ; and I know, from long experience in the term-day obser- 

 vations of the German magnetical association, how much accuracy one strives to attain, as well 

 in the instants of time as in the coincidence of the observed object with the micrometer wire 

 when he knows there are other observers whose faculties are directed to the same end at the 

 same moments, and whose results are to be competitors. 



"One other instrument will be found necessary, as well to inspire the observer with confidence 

 in his work, as to afford the means of obtaining satisfactory determinations of the planet's 

 right ascension, which may be used for comparison with the Cape of Good Hope and Paramatta 

 observatories. I mean a good astronomical clock ; for experience has taught me that the rate 

 of chronometers from day to day is not sufficiently uniform to be relied on for work so delicate. 

 Such a clock we already have, and as it is not employed on necessary service, it can doubtless 

 be obtained ; and I take it for granted that the two observatories mentioned will co-operate with 

 us as soon as they know that our station has been selected." 



A third letter from Dr. Gerling, transmitting the opinions of Gauss, Encke, and Boguslaw- 

 ski, came very shortly afterwards; and on the 24th December he again wrote me, part of which, 

 in reply to my last, is as follows : 



' Whilst I promptly acknowledge the importance of yours, and the gratitude with which it 

 inspires me, I candidly confess that the decision you ask of me respecting the proper locality 

 for the observations of 1849 gives an importance to my judgment I would not voluntarily 

 assume ; for it is evident to me that such a decision can only be properly arrived at by yourself 

 and your American friends. Yet, in your own spirit of candor, I will tell you the reflections 

 which would influence me in arriving at such determination. 



" From the greater length of the base of operations, Chiloe would possess an unquestionable 

 advantage; whilst Valparaiso really appears a preferable station, by reason of its better climate, 

 and not on account of its lying nearly on the parallel of the Cape of Good Hope, as Bogus- 

 lawski, in my opinion, erroneously adduces. I coincide with you fully that a difference of lon- 

 gitude of one or two degrees is altogether unimportant, if other benefits may be obtained by a 

 change ; and the question thus reduces itself to a comparison of the efts-advantage of shortening 

 the base with the advantage of an increase in the number of observations. Now, assuming 

 the latitude of Washington to be 38 53' north, Chiloe 43 05' and Valparaiso 33 02' south, 

 (neglecting differences of longitude,) we have Washington-Chiloe 1.312 radii of the earth, and, 

 on the other hand, Washington-Valparaiso 1.174. Consequently, this shortening of the base 

 will diminish the value of the work in the proportion 1.174 : 1.312 that is, approximately as 

 17 : 19. But if by an increase in the number of observations this unfavorable change may be 

 counterbalanced, we have to consider that (ciuteris paribus) the accuracy of the results increases 

 only as the square root of their number. Hence it will be necessary to multiply observations 

 in the proportion of 19 2 to 17 2 , or 361 : 289, or nearly as 5 : 4. Consequently, Valparaiso will 

 C 



